[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 20 from proof tree-ext (previous step)

ε ∈ dnode(md, sdt) ↔ ε ∈ dnode(md0, sdt0), ε ∈ dnode(md, sdt) → (dnode(md, sdt)[ε].dir? ↔ dnode(md0, sdt0)[ε].dir?) ∧ (dnode(md, sdt)[ε].dir? ⊃ dnode(md, sdt)[ε].meta = dnode(md0, sdt0)[ε].meta;dnode(md, sdt)[ε].fid = dnode(md0, sdt0)[ε].fid), ∀ p. (p ∈ dnode(md, sdt) ↔ p ∈ dnode(md0, sdt0)) ∧ ( p ∈ dnode(md, sdt) → (dnode(md, sdt)[p].dir? ↔ dnode(md0, sdt0)[p].dir?) ∧ (dnode(md, sdt)[p].dir? ⊃ dnode(md, sdt)[p].meta = dnode(md0, sdt0)[p].meta;dnode(md, sdt)[p].fid = dnode(md0, sdt0)[p].fid)), ∀ str. str ∈ sdt → (∀ tree2. (∀ p. (p ∈ sdt[str] ↔ p ∈ tree2) ∧ ( p ∈ sdt[str] → (sdt[str][p].dir? ↔ tree2[p].dir?) ∧ (sdt[str][p].dir? ⊃ sdt[str][p].meta = tree2[p].meta;sdt[str][p].fid = tree2[p].fid))) → sdt[str] = tree2) ⊦ dnode(md, sdt) = dnode(md0, sdt0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
⊦ ε ∈ tree
Proof step 22:
⊦ tree[ε] = tree
Proof step 23:
⊦ dnode(md, sdt).dir?
Proof step 24:
⊦ dnode(md, sdt).meta = md
Proof step 25:
∀ p. (p ∈ dnode(md0, sdt) ↔ p ∈ dnode(md0, sdt0)) ∧ ( p ∈ dnode(md0, sdt) → (dnode(md0, sdt)[p].dir? ↔ dnode(md0, sdt0)[p].dir?) ∧ (dnode(md0, sdt)[p].dir? ⊃ dnode(md0, sdt)[p].meta = dnode(md0, sdt0)[p].meta;dnode(md0, sdt)[p].fid = dnode(md0, sdt0)[p].fid)), ∀ str. str ∈ sdt → (∀ tree2. (∀ p. (p ∈ sdt[str] ↔ p ∈ tree2) ∧ ( p ∈ sdt[str] → (sdt[str][p].dir? ↔ tree2[p].dir?) ∧ (sdt[str][p].dir? ⊃ sdt[str][p].meta = tree2[p].meta;sdt[str][p].fid = tree2[p].fid))) → sdt[str] = tree2) ⊦ sdt = sdt0

Rule argument

Additional information

Used simplifier rules: nil-in: ⊦ ε ∈ tree;%nil-at: ⊦ tree[ε] = tree;%isdnode: ⊦ dnode(md, sdt).dir?;%meta: ⊦ dnode(md, sdt).meta = md;% ⊦ dnode(md, sdt) = dnode(md0, sdt0) ↔ md = md0 ∧ sdt = sdt0; (ws)